Answer:
n = 4
Explanation:
Solve for n:
5 n + 34 = -2 (1 - 7 n)
Expand out terms of the right hand side:
5 n + 34 = 14 n - 2
Subtract 14 n from both sides:
(5 n - 14 n) + 34 = (14 n - 14 n) - 2
5 n - 14 n = -9 n:
-9 n + 34 = (14 n - 14 n) - 2
14 n - 14 n = 0:
34 - 9 n = -2
Subtract 34 from both sides:
(34 - 34) - 9 n = -34 - 2
34 - 34 = 0:
-9 n = -34 - 2
-34 - 2 = -36:
-9 n = -36
Divide both sides of -9 n = -36 by -9:
(-9 n)/(-9) = (-36)/(-9)
(-9)/(-9) = 1:
n = (-36)/(-9)
The gcd of -36 and -9 is -9, so (-36)/(-9) = (-9×4)/(-9×1) = (-9)/(-9)×4 = 4:
Answer: n = 4